If any of the targets of Yosei’s ability are illegal, they won’t be tapped.

11/17/2017

If all of the permanents targeted by Yosei’s ability become illegal targets, nothing becomes tapped, but the target player still skips their untap step.

11/17/2017

If the player becomes an illegal target, the target permanents are tapped, but the player doesn’t skip their untap step.

11/17/2017

If a permanent won’t untap during its controller’s next untap step, that effect waits to apply until its controller has an untap step that isn’t skipped.

11/17/2017

If more than one effect instructs a player to skip their next untap step, such as if Yosei dies more than once in a turn, that player skips that many untap steps. This is different from effects that state that something doesn’t untap during an untap step.